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In this ongoing work, we employ persistent homology to analyze the RNA suboptimal structure space and secondary structure space of 5s rRNA. Our basic idea is to measure the topological similarity of the suboptimal structures by sliding the minimum free energy window. The preliminary result shows that the more the energy window slides from the lowest minimum energy structure the more dissimilar the structures with the lowest one. In addition, persistent homology is also used to classify 5s rRNA of Archaea species into different family of classes. Our preliminary result shows that structural dissimilarity can be observed even for species that are grouped under the same genus.